Problem: Rewrite as a simplified fraction. ${0.\overline{12} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 12.1212...\\ 1x &= 0.1212...\end{align*}}$ Subtracting the two equations, we have: ${99x = 12}$ ${x = \dfrac{12}{99}} $ ${x = \dfrac{4}{33}} $